Multiplier K/sub m//μ-analysis - LMI approach

Abstract

The theory of K/sub m///spl mu/-synthesis and analysis introduced by Safonov (1983) and Doyle (1983) essentially performs the following D-K iteration steps: 1) design a /spl Hscr//sub /spl infin//-controller K(s) such as to maximize the multivariable stabilty margin K/sub m/; and 2) for discrete frequencies, find a diagonal scaling frequency response matrix D(jw) as to maximize K/sub m/ for a fixed K(s). Step 1 can be cast as a linear matrix inequalities (LMI) optimization problem for full order controller. The K/sub m/ analysis in step 2 has been shown to be a LMI optimization problem. The paper reviews the fixed order optimal multiplier K/sub m/ analysis theory and presents state space parameterization for the set of multipliers subject to mixed dynamic and real parametric uncertainties. A numerical example involving the robustness analysis of the Cassini spacecraft thrust vector control system is also included.